The woman, who cannot be identified for legal reasons, was found to have stabbed her two sons, aged nine and 11, in their house in September 2024.
But on Thursday, NSW Supreme Court Justice Richard Cavanagh returned a special verdict of act proven but not criminally responsible due to the woman's extensive mental health impairment at the time.
The woman, now 44, and the children's father split up in 2020.
When the man told his ex-wife that his new partner was pregnant four years later, she began displaying concerning online behaviour, the agreed facts show.
She made dozens of Google searches relating to taking her own life and those of her children in the month between learning about the pregnancy and killing the boys.
A scientific article about factors in parents who kill their children and themselves was found in her phone's web history.
The woman would often text her ex-husband about everyday matters while making the concerning searches, the agreed facts state.
Less than two weeks before the boys' deaths, the woman bought two knives for her children to give their father as a Father's Day gift.
Another reason given by the woman for her mental health's deterioration was a negative ruling in the Industrial Relations Commission.
"The world is not fair," she is said to have told her psychologist a week before the killings.
She made more than thirty disturbing internet searches about violence against herself and others on the night of September 9 before entering her children's rooms with one of the knives she bought them.
Both children were stabbed multiple times.
After hearing evidence from three psychiatric experts, Justice Cavanagh agreed with both defence and prosecution lawyers that the woman could not be held criminally responsible for the killings.
The woman sat with her head bowed during the proceedings while attending via audiovisual link from custody.
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